Pappa's Restaurant is a new Italian Restaurant in town. As the only Italian restaurant in the area, it faces the following daily demand curve:
Q = 500 – 25 P
Where Q is the number of meals it serves per day and P is the average price of its meals.
The cost function of the restaurant has been estimated as follows:
TC = 200 + 8 Q + .02 Q^2
As a result of the success of Pappa's other Italian restaurants start appearing in the area. As Pappa's customers gradually start trying other (new) Italian restaurants, its demand curve gets flatter (more elastic) and shifts to the left. In reaction, Pappa's lowers its price and adjust its output to the point that, eventually, its (economic) profit disappears; It becomes equal to zero. At that point the slope of its demand curve becomes -0.03 .
Determine the new (equilibrium) average price Pappa's charges for its meals. Also,write the equation for this new (zero profit) demand curve.
MC = 8 + .04 Q
Slope of ATC = -200/Q^2 + .02
Thanks so much!
Good problem.
Let me get you pointed in the right direction. You know that:
1) firms maximize when MR=MC and MR for a perfect competitor (or nearly perfect competitor ase in this example) will be Price P.
2) ATC is simply TC/Q. So, ATC=200/Q + 8 + .02Q
3) There are zero total profits. So, average total costs ATC must equal P, which from 1) equals MC. That is:
P=MC=ATC so.
8 + .04Q = 200/Q + 8 + .02Q
Solve for Q. And everything else should fall into place.
a golf course operator must decide what greens fees to set on rounfs of golf. daily demand during the week is Pd=36-Qd/10 where Qd is the number of 18-hole round and Pd is the price per round daily demand of the weekend is Pw=50-Qw/12. as a pratical matter the capacity of the cours in 240 round per day. wear and tear of the golf course is negligible.
can the operator profit by changing different prices during the week and on the weekend ? Explain breifly. what greens fees should the operator sret on the weekdays and how many rounf will be played? on the weejend ?
To determine whether the golf course operator can profit by changing prices during the week and on weekends, we need to compare the costs and revenues associated with different pricing strategies.
First, let's determine the maximum number of rounds that can be played per day, which is the capacity of the golf course at 240 rounds.
On weekdays:
The demand equation for weekdays is Pd = 36 - Qd/10
To maximize revenue, the operator should set price Pd equal to marginal revenue (MR), which is Pd = MRd.
So, Pd = 36 - Qd/10.
On weekends:
The demand equation for weekends is Pw = 50 - Qw/12
To maximize revenue, the operator should set price Pw equal to marginal revenue (MR), which is Pw = MRw.
So, Pw = 50 - Qw/12.
Since wear and tear of the golf course is negligible, the operator's only consideration is maximizing revenue. The operator should charge the highest possible price that customers are willing to pay on both weekdays and weekends.
To determine the number of rounds played on each day, we need to consider capacity constraints. Since the golf course can accommodate a maximum of 240 rounds per day, the total number of rounds played on weekdays and weekends should not exceed this limit.
Now, let's determine the optimal pricing and number of rounds for weekdays and weekends:
Weekdays:
The operator should set price Pd (weekday greens fees) to maximize revenue:
Pd = 36 - Qd/10
To determine the number of rounds played on weekdays, we subtract the maximum capacity from the optimal quantity:
Qd = 240 - Qw
Substituting this in the demand equation for weekdays:
Pd = 36 - (240 - Qw)/10
Weekends:
The operator should set price Pw (weekend greens fees) to maximize revenue:
Pw = 50 - Qw/12
The number of rounds played on weekends is simply Qw.
By solving these equations, we can find the optimal prices and number of rounds played on weekdays and weekends.